VLC supports bookmarking (Just press CTRL+B), but this is not an automatic thing that happens if you close VLC. I doubt any player has an automatically save position when player is exited feature.. not sure about that.
actually … adobe's media-player(ver 1.8) seems to have the feature being discussed. person can watch one video and select "pause" … close program or quit program from system-tray … even switch to another video … when you return to that previous video, it will resume where it had been paused. i should explain a bit further … the videos i tried were on my hard-drive and were located in my "favorites/personal-videos" within the program interface. have att'd screen-cap for clarification of adobe's interface.
edit: wanted to add one other suggestion. be cautious when downloading the software … copy/paste the url to virus-total website so it can make sure the link has a clean file for download … further, verify you fully scan the program once it's on your hard-drive … and, if i were you, i'd create system-restore point before installation.